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Math Help - Simplifying Ln(x)

  1. #1
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    Simplifying Ln(x)

    Hey all i'm having a tough time simplifying this:

    nln(1/y1)-nln(1/y2)+((1/y1)-(1/y2))(ln(x1)+ln(x2)+...ln(xn))

    yuck!
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  2. #2
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    Re: Simplifying Ln(x)

    I can't say what you would consider "simpler" but, using the properties of logarithms, that is
    ln\left(\left(\frac{y_2}{y_1}\right)^n\left(x_1x_2  \cdot\cdot\cdot xn\right)^{\frac{y_2- y_1}{y_1y_2}}\right)
    Thanks from VanBuren
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  3. #3
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    Re: Simplifying Ln(x)

    [FONT=Arial]Hey thanks for the speedy response, this is actually a smaller part of a much larger stats question I have....

    chi-squared distribution=


    with

    where Y is actually theta

    I need to develop a method for testing H0 : θ = θ0 against H0 : θ = θ1 where 0 < θ0 < θ1 < 1
    But i'm stuck, i plugged the moment generating function into the formula for chi-squared but have no idea if simplifying is even the right direction... i'm not dumb i'm just stuck... help!
    Last edited by VanBuren; May 9th 2012 at 06:25 PM.
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  4. #4
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    Re: Simplifying Ln(x)

    Here is the likelihood function of Y sub whatever:

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